Deriving PDF from a given signal without using the hist() function?

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catarina 2011-12-29

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Hello,

       I'm newbie at this and am enjoyably although a bit painfully trying to work my way around Matlab. As my question implies I have a signal and I would like to derive it's PDF function numerically without using the hist () function ? I looked in the documentation that it would be:
    p1=pdf('name',X,A)  or extra B,C depending if we have 1 or three parameters. Although I read the documentation I don't understand what X stands for (what I should replace it with?). From what I understand if it's for example normal pdf it would be:
    p1=(pdf('name', X, A, B), being A the mean and B the standart derivation and X I don't know.  I really don't understand how do I relate the pdf function with the signal I generated on matlab???
   Hope I'm making sense and someone is able to help.
   Thank you very much
   Catarina

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Answer 1

bym 2011-12-29

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在 MATLAB Online 中打开

I am not sure I understand, but take a look at:

doc ksdensity

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David Young 2011-12-30

catarina: I'm very puzzled. If you can't use hist(), how is that ksdensity() is a good solution?

King Fisher 2012-1-27

Thanks proecsm ! you helped in solving my issue as well !

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Answer 2

David Young 2011-12-29

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The pdf function is not useful for this. It generates the theoretical PDF for a named distribution, but does not estimate an empirical PDF from data.

You are probably being asked to write code that does what hist does. This involves taking each element of the signal vector, working out the index of the bin it falls into, and incrementing an element of a histogram vector. To get an estimated PDF, you'd finally normalise the counts in the histogram vector.

You can do this with loops, or using MATLAB's vectorised style of programming. The essential ideas are the same in both cases, but vectorised code is more compact and often somewhat more efficient.

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David Young 2011-12-30

Yes, my answer still applies. You are being asked to generate some synthetic data, and then estimate some results from it. So the first part is to generate the signal numerically, which in MATLAB can be done like this:

f = 2500;

deltaT = 0.0001;

Tmax = 0.01;

t = 0:deltaT:Tmax;

x = 4-cos(2*pi*f*t);

Here, I've just made up values for deltaT (the time increment between samples) and Tmax (the duration of the signal). As you can see, it's a matter of getting a vector of time values, and then applying the formula you were given to it.

Now you have x, your "data", from which you can estimate parameters numerically. For example, you can get the signal mean with

mean(x)

The fact that you are asked not to use the hist function for the PDF confirms, I think, that you are expected to write code that does roughly the same as hist. This involves counting how many values of x occur in a set of ranges. One approach: see what happens when you call hist(x), understand how that relates to the PDF, and then write code to produce the same results.

catarina 2012-1-26

Hi David (and other people that might be able to help),

I'm still having problems in deriving the PDF without the hist() function but I think is because I'm stuck in how to code certain stuff. Would you able to look at my script and if possible give me some tips? I explained my doubts in the script.

Here is my script:

%Estimating PDF numerically without using hist() function

%Dividing amplitude range into M=60 segments

delta=20 %Amplitude range

n=0:1:M-1;

An=-10+n*(delta/M);

%sampling the signal

%Time points

N=1024; %(number of samples)

j=0:1:N-1;

T=1; %(number of cycles for tis problem T=1)

tj=j*(T/N)

%function points

yj=10*sin(2*pi*tj);

%counting number of samples falling in each segment:

%by constructing a 2D array with elements defined as:

%fnj={1, if An<=yj<=An+1,0 otherwise - I'm not being able to represent

%this statement in matlab, I tried using if statements

%but keeps giving me an error

%Counting the number of samples Fn in amplitude segment number n as:

% N-1

% Fn=sigma(fnj) -not able to represent this in matlab code

% j=0

%Now plot Fn agains An - can't do this because of my previous the doubts

Cheers,

Catarina

Walter Roberson 2012-1-27

No point debugging this in two Questions. See the answer in your newer Question on this point, http://www.mathworks.com/matlabcentral/answers/27188-estimating-pdf-numerically-without-using-hist-function

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Answer 3

Peter Perkins 2011-12-29

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Catarina, the pdf function (I assume this is the one in the Statistics Toolbox) evaluates a known PDF at a set of points. That isn't what you want, at least initially.

If you have a set of data, then I think what you're asking for is a way to estimate their PDF. For a normal distribution, that's the normfit function, for other distributions there are other corresponding functions. Once, you have estimated the parameters of the distribution you want to use, then you can use the pdf function to plot the PDF over some range. There is also the ksdensity function, which creates a non-parametric estimate.

You might find it easier to use the fitdist function, and even easier still to use dfittool, which lets you do all this using a GUI.

Hope this helps.

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David Young 2011-12-30

Peter: I suspect the fact that hist() is mentioned is an indication that the empirical PDF based on the histogram is required, not a fit to a specific model. Since hist() is forbidden, and the object is to become familiar with MATLAB rather than analyse some real data, I doubt that ksdensity() will be the right kind of answer.

King Fisher 2012-1-27

u r right ! david !

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